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phy 121
Your 'cq_1_17.2' report has been received. Scroll down through the document to see any comments I might have inserted, and my final comment at the end.
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A 5 kg cart rests on an incline which makes an angle of 30 degrees with the horizontal.
• Sketch this situation with the incline rising as you move to the right and the cart on the incline. Include an x-y coordinate system with the origin centered on the cart, with the x axis directed up and to the right in the direction parallel to the incline.
The gravitational force on the cart acts vertically downward, and therefore has nonzero components parallel and perpendicular to the incline.
Sketch the x and y components of the force, as estimate the magnitude of each component.
What angle does the gravitational force make with the positive x axis, as measured counterclockwise from the positive x axis? Which is greater in magnitude, the x or the y component of the gravitational force?
answer/question/discussion: ->->->->->->->->->->->-> :
The force of gravity acting on the 5kg cart is 5*9.8m/s^2 = 49N If we’re trying to find the x and y components of the force vector we say
Fx= Fcos(theta)
Fx = (49N)cos(30degrees) = 42.4N
Fy = Fsin(theta)
Fy = (49N)sin(30degrees) = 24.5N
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• Using the definitions of the sine and cosine, find the components of the cart's weight parallel and perpendicular to the incline.
answer/question/discussion: ->->->->->->->->->->->-> :
Using the Pythagorean theorem we can find the magnitude of the force vector which may or may not be what you are asking for here.. in any case
Magnitude = `sqrt [x^2 + y^2]
Magnitude = `sqrt [42.4N^2 + 24.5N^2\
= `sqrt 2398.01
= 48.9N
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• How much elastic or compressive force must the incline exert to support the cart, and what is the direction of this force?
answer/question/discussion: ->->->->->->->->->->->-> :
From my equations sheet I see that the
PEelastic = ˝ k*x^2 however im not sure if this is the equation I should be using since I don’t know what the restoring force constant, or position is.
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You don't have any information about the effective value of k, and don't care much about the deformation x, which for the ramp will be small.
The point is that the incline will exert whatever force is needed to keep the cart from falling through it.
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• If no other force is exerted parallel to the incline, what will be the cart's acceleration?
answer/question/discussion: ->->->->->->->->->->->-> :
Im sure I need the quantities from the previous questions to properly answer this one, in which case I will wait for notes and submit revisions.
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about 20 minutes
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Good start.
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Solution
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